The Topological Structure And Continuity In Concept Lattice And Generic Concept Lattice

The concept of formal context derived from philosophy is constituted byextension and intension. In order to realize the discovering, ranking and displayingof the concept, based on formal context, German mathematician Will.R frist proposethe structure lattice theory, since then, it has become an important method of dataanalysis.After the concept of the conceptual knowledge system was given, we prove thatthe formal context and conceptual knowledge system can determine each other. Andthe connection between the conceptual knowledge system and closure system wasestablished.At the same time, the method of generating concept and generic concept informal context was given in this paper. Based on the upper and lower orderhomomorphism, we study the upper and lower order homomorphism of the conceptlattice and generic concept lattice. Furthermore,we also discuss the upper andlower continuity as well as upper and lower generic continuity.Finally,applying the continuity of the ordinary topologies spaces,we analysisthe the continuity of concept lattice on some ordinary topological spaces which arederived from the upper and lower case topological.In addition,we establish theequivalence of the continuity between the upper and lower case topological spacesand the continuity on the general topological spaces of concept lattice.